Which of the following numbers is a multiple of 2? ${60,81,87,95,105}$
The multiples of $2$ are $2$ $4$ $6$ $8$ ..... In general, any number that leaves no remainder when divided by $2$ is considered a multiple of $2$ We can start by dividing each of our answer choices by $2$ $60 \div 2 = 30$ $81 \div 2 = 40\text{ R }1$ $87 \div 2 = 43\text{ R }1$ $95 \div 2 = 47\text{ R }1$ $105 \div 2 = 52\text{ R }1$ The only answer choice that leaves no remainder after the division is $60$ $ 30$ $2$ $60$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $2$ are contained within the prime factors of $60$ $60 = 2\times2\times3\times5 2 = 2$ Therefore the only multiple of $2$ out of our choices is $60$. We can say that $60$ is divisible by $2$.